1. Field of the Invention
The present invention relates generally to band gap voltage reference cells and more particularly to such cells which precisely and fundamentally compensate for a nonlinear response arising from temperature variations and which generate a higher or lower output voltage than a conventional implementation.
2. Description of the Related Art
The ubiquitous "band-gap" principle finds widespread usage not only in voltage references for converters and other highly calibrated circuits, but also as the most convenient basis for simply setting up a bias (voltage or current) which is supply and temperature independent and of moderate accuracy. One such circuit in which the principle is applied is disclosed in U.S. Pat. No. 3,887,863 and U.S. Pat. No. Reissue 30,586 to Brokaw for a solid-state regulated voltage supply. Such circuits use forward-biased PN junctions operated at differing current densities; most usually, bipolar transistors having a reliable relationship between collector current (I.sub.C) and base-emitter voltage (V.sub.BE) are utilized.
The most common realization generates a loadable output voltage, usually some 65 mV greater than the so-called "band-gap voltage", which is referred to as E.sub.GE herein, corresponding to EG in SPICE. The e is added to E.sub.G to indicate that this is an effective or empirical quantity with the dimension of voltage. It is not a fundamental and directly-accessible physical constant, although it is closely related to the intrinsic zero-temperature band-gap energy of silicon. Such things as lattice strain, doping level and temperature all affect E.sub.GE, which is best viewed as a process-dependent characterization parameter. It is determined by measuring V.sub.BE over a range of temperatures followed by curve-fitting. The well-known starting-point for V.sub.BE (T) is given in many texts as: EQU V.sub.BE (T)=Vtln(Ic/AJs(T)) Eq (1)
where Vt=kT/q is the thermal voltage which equals 25.85 mV at 300 K., Ic is the collector current, A is the emitter area and Js(T) is the strongly temperature-dependent saturation current-density. This form, however, is not very satisfactory, because it doesn't explicitly include E.sub.GE, it obscures the simple basic shape of V.sub.BE (T), and it is impractical to parametize. A more useful formulation, obtained by analytically using a comprehensive expression for Js(T), followed by a practical characterization procedure is: EQU V.sub.BE (H)=E.sub.GE -H(E.sub.GE -V.sub.BER)+HVtr(ln(Ic/Ir)-m ln H)Eq (2)
where V.sub.BER is the V.sub.BE for a known collector current Ir and reference temperature Tr, Vtr is the value of Vt at this reference temperature, m is the exponent of temperature in the full expression for Js(T), which is called XTI in SPICE, and has a theoretical value of 3.5.
In Equation (2), H=T/Tr. This conveys the idea of relative "hotness" and avoids the needless repetition of quotient factors (T/Tr). Thus, H is 1 when the junction temperature is the same as the reference temperature; H is zero at absolute zero of temperature; and is roughly 2 in the extrapolated temperature region where V.sub.BE approaches to zero. The components of V.sub.BE (H) can be expressed as follows: EQU V.sub.BE (H)=E.sub.GE -H{E.sub.GE -V.sub.BER -Vtr ln(Ic/Ir)}-mVtrH ln HEq (2a)
where the first term is a fixed voltage, the second term is a linearly-decreasing voltage and the third term represents the "curvature." To parametize the V.sub.BE expression, the device is operated at some moderate level of current, preferably but not necessarily at Ic=Ir, avoiding either low- or high-injection operating regions, and at some moderate value of collector bias, and V.sub.BE is measured over temperature, from which data E.sub.GE and m can be determined by nonlinear regression; typical values are E.sub.GE =1.2 V and m=3.5.